yes. He and Miss Schumann often used to stay after school and work in there. It was all quite proper, too. My hours are from nine to five, you see, so when my time was up, and the library key hadn’t come back to my office, I had to go along and get it from them, so that all the school keys could be locked away. That was part of my job. The two of them were always working. She would mostly be doing her marking and he would be studying and making notes. When I had to interrupt them he never had to put any of his books back on the shelves, because they didn’t belong to the school.’

‘You wouldn’t know whether they came from the public library, I suppose?’

‘I expect most of them did, in the early days, but some he borrowed from Miss Schumann’s mother. I know that, because one day, when he was slinging them into his bag and arguing his head off about some pope or bishop or something, he dropped one, and she told him to be careful, otherwise her mother wouldn’t lend him any more of her father’s books. Quite annoyed with him, she was, and, of course, being a man, he didn’t like being ticked off in front of me, so he said, “My misguided little something or other …”’

‘Aryan?’

‘That’s right – “your father’s books are at least being put to some use again”. She was mad with him. “Not by being dropped on the floor,” she said, “and I’ll thank you for not referring to me as a Nazi!” He stared a bit at that, then he gave a nasty little snigger and said, “Oh, were they the fore-runners? I had no idea!” I thought it was time to break it up, so I asked for the key, saw them out, locked up and went home.’

Dame Beatrice had only one more question to ask.

‘Does Mr James read German, then?’

‘Oh, yes, and speaks it, too. It annoyed some of the others, because he and Miss Schumann used to talk to each other in German in the Common Room. The others thought it was just a bit of show-off, because, of course, Miss Schumann, who was born and brought up over here, could speak perfect English. Anything else I can tell you? I only ask because I don’t like leaving Derry too long, although he loves the dog, of course.’

Dame Beatrice said that there was nothing else she wanted to ask. She thanked Mrs Clancy and was invited to come again at any time. She took her leave and went back to the Kensington house, where she found Laura scowling at a piece of graph paper covered with scribbled figures, weird doodles and shorthand symbols. She looked up as Dame Beatrice came in, and pushed the paper away.

‘How did you get on?’ she asked.

‘A glimmer of light is discernable, but, of course, it may be no more than a will o’ the wisp. Your own train of thought appears to be of a complicated and unsatisfactory nature – or are you casting spells?’

‘I’ve been trying to work out a problem in progressions, but it won’t jell.’

‘In progressions?’

‘Yes. You see, we’ve now got three sets of figures to play with, and three nationalities, so I ought to be able to work out the next step, but I can’t. Three hundred and twenty-five and three hundred and eighty and eleven hundred and fifty-five don’t make any sense at all. Of course, mathematics was never my life’s work.’

‘There is a number common to all, in one sense.’

‘Yes, the fifty-five bit. Three hundred and twenty-five from three hundred and eighty leaves fifty-five, and that comes after the eleven hundred, but I can’t get any further.’

‘Divide the fifty-five by the eleven, ignoring zero. The result, if you are well versed in the multiplication table, is five.’

‘So what?’

‘So we may expect two more of these extraordinary murders, making five in all.’

Laura made a face at her.

‘All flippancy aside, though,’ she said, ‘did you really find out something useful this afternoon?’

‘I do not know yet whether what I found out was useful, but it certainly was quite interesting. James was in the habit of working in the school library in his own time, so he may be speaking the truth about the way he spent that day. He borrowed theological treatises from Mrs Schumann’s late husband’s library, so he may have visited her cottage more often than we were led to suppose.’

‘More often than Mrs Schumann admitted, you mean?’

‘I think it would be unfair to put it like that. We asked how often he spent the week-end there with his fiancée, I believe. The answer Mrs Schumann gave was no doubt perfectly truthful.’

‘She could have added the other bit, though, couldn’t she? – that sometimes he went when Karen wasn’t there.’

‘It may not have occurred to her to do so. Actually, why should it? One more tiny point emerged. You remember Mrs Schumann’s telling us of her daughter’s indignation when Edward James called her a misguided little Aryan?’

‘Yes. It seemed an odd sort of remark to make. We thought so at the time.’

‘We did know that they were having a theological discussion, but that remark was concluded in a way that Mrs Schumann did not tell us because I am sure her daughter did not see that it had any significance and therefore, being full of what she regarded as the insult of being called an Aryan, did not think worth repeating.’

‘What was this significant addition?’

‘Mrs Clancy, who was present, said that James sniggered and added, “Oh, were they the forerunners? I had no idea!”’

‘Forerunners of what?’ asked Laura.

‘The Nazis.’

‘Doesn’t seem a very profound remark to me.’

‘It turns on the word Aryan.’

‘You speak in riddles, as ever. Tell me more.’

‘Oh, no,’ said Dame Beatrice. ‘You work it out for yourself. Or, rather, you can go to the public library and work it out there. James studied history as well as

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